Undersaturated isothermal oil compressibility

Undersaturated isothermal oil compressibility is defined as the unit change of volume with pressure at constant temperature. When the oil compressibility is used in the calculation of undersaturated oil density or FVF above bubblepoint pressure the following equation is applied:

1. Standing (1947)
$${\overline{\text{c}}}_{\text{o}}=\frac{\text{1}}{\text{p}-{\text{p}}_{\text{b}}}{\displaystyle \underset{{\text{P}}_{\text{b}}}{\overset{\text{P}}{\int }}{\text{c}}_{\text{o}}\text{(p)dp}}$$

To avoid the calculation involved in the equation above, the average oil compressibility can be calculated at average pressure, i.e. Co is evaluated at

$$\overline{P}=\left(\frac{\text{P}+{\text{P}}_{\text{b}}}{\text{2}}\right)$$

as follows:

$${\overline{\text{c}}}_{\text{o}}={\text{c}}_{\text{o}}(\overline{P})$$

Three methods for estimating undersaturated isothermal oil compressibility are presented.

2. Vasquez & Beggs (1980)
$$C_O=(a_1+a_2{R}_s+a_{3}T+a_4{\gamma }_g+a_5{\gamma }_{API})/p$$ $$\overline{)\begin{array}{}\text{Coefficient}\text{Original}\\ a_1& -14.33x{10}^{-3}\\ a_2& 50x{10}^{-6}\\ a_3& 0.172x{10}^{-3}\\ a_4& -11.80x{10}^{-3}\\ a_5& 0.1261x{10}^{-3}\end{array}}$$




3. Petrosky and Farshad (1993)
$${\text{c}}_{\text{o}}={\text{a}}_{\text{1}}{\text{R}}_{\text{s}}^{{\text{a}}_{\text{2}}}{\text{γ}}_{\text{g}}^{{\text{a}}_{\text{3}}}{\text{γ}}_{\text{api}}^{{\text{a}}_{\text{4}}}{\text{T}}^{{\text{a}}_5}{\text{P}}^{{\text{a}}_{\text{6}}}$$ $$\overline{)\begin{array}{}\text{Coefficient}\text{Original}\\ a_1& 0.1705x{10}^{-6}\\ a_2& 0.69357\\ a_3& 0.1885\\ a_4& 0.3272\\ a_5& 0.6729\\ a_6& -0.5906\end{array}}$$




4. Al-Marhoun (2003)
$$\ln c_o=a_1+a_2/{\gamma }_{ob}+a_3(P-P_b)/{\gamma }_{ob}^3+a_4/(T+460)$$

where

$${\gamma }_{ob}=({\gamma }_o+2.18x{10}^{-4}{R}_s{\gamma }_g)/B_{ob}$$ $$\overline{)\begin{array}{}\text{Coefficient}\text{Original}\\ a_1& -14.1042\\ a_2& 2.7314\\ a_3& -56.0605x{10}^{-6}\\ a_4& -580.8778\end{array}}$$